Dataset Capstone

To Do

• Fix links

• Make a gif of pymeanshift samples with variables/stats

• Visualize color values

Overview

Summary

Photography has been a hobby of mine for most of my life, and I found a particular niche in abstract photography, specifically multi-exposure images. This background inspired me to find mathematical ways to analyze my photo library as a whole, with a special focus on color trends and affinities.

Business Application

The processes used in this project have a business application within a mobile app. By evaluating a user’s camera roll, the app could discern favorite colors and suggest products that match that color profile.

Data Collection Method

Flickr API

• Worked backwards from the present to separate generic images (downloads, memes, screenshots, videos) from photos (robust EXIF data)
• Collected 4500 usable flickr IDs (more IDs meant a larger date range to sample from)
  • (Python script was used to randomly select from the mega-list)
• Selected IDs had their EXIF data collected (again) and jpg downloaded at “XL” size
• EXIF data was saved to its own CSV

Python

• Each photo was mathematically divided into 9 subimages, to allow for full-photo trends to be compared against center-image trends
  • (All calculations were done on each photo 10 times, once for the full photo, and once for each sub-image. In retrospect, much of the sub-image processing was redundant and could have been gathered via subsetting the full-image matrix)
• Gamma adjustment (RGB linearization)
  • https://en.wikipedia.org/wiki/SRGB#Transfer_function_(%22g`amma%22
• Conversion to HSL for “readable” values (colorsys library)
• Segmentation (“posterization”) (pymeanshift library)
  • https://github.com/fjean/pymeanshift

Note:

Shout out to my buddy Phil! He was a great resource for feedback and encouragement as I formulated my processing script, but also donated runtime on his computer and processed 250 images used in this dataset.

PyMeanShift/Segmentation

A photograph with 4000 pixels may have 4000 different color values represented. I wanted to “clump” pixels with similar colors in the same area of an image into a single color value. PyMeanShift accomplishes this by taking in the image and three numerical variables: spatial radius, range radius, and minimum density. These refer to maximum color difference, maximum placement difference, and minimum “clump” size, respectively.

https://ieeexplore.ieee.org/document/1000236

Datapoints Collected

EXIF

FlickrID - unique identifier for each photo

DateTimeOriginal/CreateDate/ModifyDate - attempted to capture whether the images were edited on the phone (unsuccessful)

Software - iOS version or mobile app used for photo capture

LensInfo/ LensModel - data on which phone lens capture the photo

JFIFVersion - compression marker applied by some 3rd party apps. Disappears when image is edited in native iOS photos app.

ISO - light sensitivity setting

ExposureTime - in seconds (fractions)

FNumber - aperture

FocalLength- Fixed to LensInfo/LensModel

FocalLengthIn35mmFormat - iOS interpretation of zoom level

BrightnessValue - Auto-generated brightness value

SubjectArea -  Coordinate values generated by iOS (not directly relevant to this project, but captured for future use)

Image Data

A python class was used to gather image data as attributes, then dumped to a csv with vars(). 

All relevant attributes/variables described below

using_id - Flickr ID

img_width - in pixels

img_height - in pixels

do_img_at - timestamp for evaluating processing time 

sub_img - 0 for whole image, 1 for top-left, 2 for middle-left, 5 for center, etc.

full_id - concat of flickrID and sub_image to form unique identifier.

RGB Overview Statistics

(r/g/b)_min - (3 columns) Minimum red/green/blue channel value in the whole image

(r/g/b)_max - (3 columns) Maximum red/green/blue channel value

(r/g/b)_mean - (3 columns) Average red/green/blue channel value

(r/g/b)_mode - (3 columns) count of common red/green/blue channel value (forgot to capture its value :facepalm: (in my attempt to capture the value, I neglected to reset the index of the pandas dataSeries))

center_rgb - (tuple) R/G/B value of the pixel mathematically in the center of the image

Next segment of columns captured from segmented/posterized image

post_num_regions - number of color “clumps” after processing

post_top_hsl - (tuple) most common pixel value

post_top_count - quantity of most common pixel value

post_(2-6)_hsl - (5 columns)(tuples) next most common pixel values, in descending order of frequency

post_(2-6)_count - (5 columns) counts for their respective common pixel values

center_hsl - (tuple) HSL value of the pixel mathematically in the center of the image

Hue color banding was done by subjective eyeball measurement

All hues: red, orange, yellow, green, cyan, blue, purple, magenta

full_(hue)_count - count of all pixels that fell within the hue band, regardless of saturation and lightness

visib_(hue)_count - count of pixels in the hue band deemed as “visibly [hue]” (saturation over 40%, lightness between 20% and 75%)

vivid_(hue)_count - count of pixels in the hue band deemed as “vividly [hue]” (saturation over 70%, lightness between 30% and 70%)

Saturation Statistics

sat_min_val - lowest saturation value in image

sat_25_val - 25% quartile value

sat_50_val - median saturation

sat_75_val - 75% quartile value

sat_max_val - most saturation

HSL Mean Values

hue_mean_val - average hue value (not incredibly meaningful on a looping spectrum)

sat_mean_val - average saturation value

light_mean_val - average brightness

Lightness Statistics

light_max_val - brightest value

light_max_count - quantity of pixels within 1.5% (literal) of the max lightness value

light_min_val - darkest value

light_min_count - quantity of pixels within 1.5% (literal) of he minimum lightness value (darkest)

light_25_value - 25% quartile value

light_50_value - median brightness

light_75_value - 75% quartile value

gen_bright_count - quantity of pixels with over 85% lightness

gen_dark_count - quantity of pixels with under 15% brightness

common_hsl_(1-4)_val - (4 columns)(tuple) four most common HSL values

common_hsl_(1-4)_count - (4 columns) quantities of the four most common HSL values

Data Collation

Due to collecting image processing data on multiple computers, multiple files were created for exif and image data – partly by design and party due to occasional read/write conflicts on shared files. All records were gathered into Excel and checked for duplicates before exporting as CSVs.

Hypotheses

H1 - Hue vs Date

\(Ho:\) There is no correlation between time of year and color values

\(Ha:\) Warm color values are more prominent between May and September

H2 - Lightness vs Time

\(Ho:\) There is no correlation between time of day and lightness values

\(Ha:\) Lightness values are higher between 6 am and 6pm

H3 - Saturation vs Subject

\(Ho:\) There is no correlation between saturation and being a picture of my cat

\(Ha:\) Low saturation values are increasingly common over time, especially in central sub-images

H4 - Vividness vs Image Type

\(Ho:\) Vivid ratio (percentage of vivid pixels) is uniformly distributed among all Software types

\(Ha:\) Vivid ratio is consistently highest in Slow Shutter Cam photos without JFIF values

R

Preparing the Data

Imports

library(tidyverse)
library(plotly)
library(reshape2)

exif <- read_csv("capstone_exif.csv")
img_data <- read_csv("capstone_img_data.csv")

# spec(exif)
# spec(img_data)

Cleaning

Pre Import:
Sub-image data for main images (0) was bugged in the first hours of image processing. This was fixed in Excel during the data collation stage.

EXIF:

• Fix column headers
• Drop columns: date_time_original, modify_date, lens_info, f_number, focal_length
• NA values - JFIF <- 0,  subject_area <- >depends on data type< “0 0 0 0”

names(exif) <- gsub("([a-z0-9])([A-Z])", "\\1_\\2", names(exif))
names(exif) <- names(exif) %>% tolower()

exif_tidy <- select(exif, -c(date_time_original, modify_date, lens_info, fnumber, focal_length))
exif_tidy <- replace_na(exif_tidy, list(subject_area = "0 0 0 0", jfifversion = 0))

Img_data:

• Drop columns: flickr, img_loc, the_image, crop_coords, r_mode, b_mode, g_mode, img_height, img_width, do_img_at
• Na values - post_2-6_hsl <- (-1,-1,-1)

imgsd_tidy <- select(img_data, -c(flickr, img_loc, the_image, img_width, img_height, crop_coords, do_img_at, r_mode, b_mode, g_mode))

imgsd_tidy <- replace_na(imgsd_tidy, list(
  post_2_hsl = "(-1, -1, -1)",
  post_3_hsl = "(-1, -1, -1)",
  post_4_hsl = "(-1, -1, -1)",
  post_5_hsl = "(-1, -1, -1)",
  post_6_hsl = "(-1, -1, -1)"
  )
  )

Basic Feature Engineering

EXIF

• Split date_time_original to year, month-day, time columns
• Date column uses a placeholder year so month-to-month comparisons are consistent

exif_tidy <- exif_tidy %>% separate(create_date, into = c('full_date', 'time'), sep = " ", remove = TRUE) %>% separate(full_date, into = c('year', 'month', 'day'), sep = ":", remove = FALSE) 

exif_tidy$date <- as.Date(paste("1881", exif_tidy$month, exif_tidy$day, sep = "-"), format ="%Y-%m-%d")

Img_data

• Count by flickr id

  • Add count(flickr_id) to EXIF
  • Flag counts under 10
  • Flag counts under 6 (ie: subimage 5 not available)
  • Output list of all flickrIDs with less than 10 records for additional (future) processing

subimg_qty <- imgsd_tidy %>% count(using_id)

To my (happy) surprise, only 5 images have less than 10 results and only 2 have less than 6. In the interest of time, I’m noting these IDs by hand and simply removing them from my working data

good_ids <- subimg_qty[subimg_qty$n >=6, "using_id"]

imgsd_tidy <- imgsd_tidy %>% filter(using_id %in% good_ids$using_id)

exif_tidy <- exif_tidy %>% filter(flickr_id %in% good_ids$using_id)

• Split pixel lists/tuples for 3-d mapping (solely the domain of part 1)

• (Re)set count values as integers

• Total pixels = full_(hue)_count(s) (dimension data incorrect for first 1400 records)

• Generate ratio columns

# after working with this data for 12 hours, I find out there are hidden characeters in my data that were not displaying in Excel.

imgsd_tidy$post_top_count <- as.integer(imgsd_tidy$post_top_count)
imgsd_tidy$post_2_count <- as.integer(imgsd_tidy$post_2_count)
imgsd_tidy$post_3_count <- as.integer(imgsd_tidy$post_3_count)
imgsd_tidy$post_4_count <- as.integer(imgsd_tidy$post_4_count)
imgsd_tidy$post_5_count <- as.integer(imgsd_tidy$post_5_count)
imgsd_tidy$post_6_count <- as.integer(imgsd_tidy$post_6_count)

imgsd_tidy$common_hsl_1_count <- as.integer(imgsd_tidy$common_hsl_1_count)
imgsd_tidy$common_hsl_2_count <- as.integer(imgsd_tidy$common_hsl_2_count)
imgsd_tidy$common_hsl_3_count <- as.integer(imgsd_tidy$common_hsl_3_count)
imgsd_tidy$common_hsl_4_count <- as.integer(imgsd_tidy$common_hsl_4_count)

imgsd_tidy$full_red_count <- as.integer(imgsd_tidy$full_red_count)
imgsd_tidy$full_orange_count <- as.integer(imgsd_tidy$full_orange_count)
imgsd_tidy$full_yellow_count <- as.integer(imgsd_tidy$full_yellow_count)
imgsd_tidy$full_green_count <- as.integer(imgsd_tidy$full_green_count)
imgsd_tidy$full_cyan_count <- as.integer(imgsd_tidy$full_cyan_count)
imgsd_tidy$full_blue_count <- as.integer(imgsd_tidy$full_blue_count)
imgsd_tidy$full_purple_count <- as.integer(imgsd_tidy$full_purple_count)
imgsd_tidy$full_mag_count <- as.integer(imgsd_tidy$full_mag_count)
imgsd_tidy$visib_red_count <- as.integer(imgsd_tidy$visib_red_count)
imgsd_tidy$visib_orange_count <- as.integer(imgsd_tidy$visib_orange_count)
imgsd_tidy$visib_yellow_count <- as.integer(imgsd_tidy$visib_yellow_count)
imgsd_tidy$visib_green_count <- as.integer(imgsd_tidy$visib_green_count)
imgsd_tidy$visib_cyan_count <- as.integer(imgsd_tidy$visib_cyan_count)
imgsd_tidy$visib_blue_count <- as.integer(imgsd_tidy$visib_blue_count)
imgsd_tidy$visib_purple_count <- as.integer(imgsd_tidy$visib_purple_count)
imgsd_tidy$visib_mag_count <- as.integer(imgsd_tidy$visib_mag_count)
imgsd_tidy$vivid_red_count <- as.integer(imgsd_tidy$vivid_red_count)
imgsd_tidy$vivid_orange_count <- as.integer(imgsd_tidy$vivid_orange_count)
imgsd_tidy$vivid_yellow_count <- as.integer(imgsd_tidy$vivid_yellow_count)
imgsd_tidy$vivid_green_count <- as.integer(imgsd_tidy$vivid_green_count)
imgsd_tidy$vivid_cyan_count <- as.integer(imgsd_tidy$vivid_cyan_count)
imgsd_tidy$vivid_blue_count <- as.integer(imgsd_tidy$vivid_blue_count)
imgsd_tidy$vivid_purple_count <- as.integer(imgsd_tidy$vivid_purple_count)
imgsd_tidy$vivid_mag_count <- as.integer(imgsd_tidy$vivid_mag_count)
imgsd_tidy$vivid_count <- as.integer(imgsd_tidy$vivid_count)

imgsd_tidy$gen_bright_count <- as.integer(imgsd_tidy$gen_bright_count)
imgsd_tidy$gen_dark_count <- as.integer(imgsd_tidy$gen_dark_count)

imgsd_tidy <- imgsd_tidy %>% mutate(total_pixels = full_red_count +
                                      full_orange_count +
                                      full_yellow_count +
                                      full_green_count +
                                      full_cyan_count +
                                      full_blue_count + 
                                      full_purple_count +
                                      full_mag_count)

# more type conversions
imgsd_tidy$total_pixels <- as.integer(imgsd_tidy$total_pixels)
imgsd_tidy$light_mean_val <- as.numeric(imgsd_tidy$light_mean_val)
imgsd_tidy$post_num_regions <- as.integer(imgsd_tidy$post_num_regions)
imgsd_tidy$r_mean <- as.numeric(imgsd_tidy$r_mean)
imgsd_tidy$g_mean <- as.numeric(imgsd_tidy$g_mean)
imgsd_tidy$b_mean <- as.numeric(imgsd_tidy$b_mean)


#establishing ratio columns
imgsd_ratio <- imgsd_tidy %>% 
  mutate(ratio_post_top_hsl = post_top_count / total_pixels) %>%
  mutate(ratio_post_2_hsl = post_2_count / total_pixels) %>%
  mutate(ratio_post_3_hsl = post_3_count / total_pixels) %>%
  mutate(ratio_post_4_hsl = post_4_count / total_pixels) %>%
  mutate(ratio_post_5_hsl = post_5_count / total_pixels) %>%
  mutate(ratio_post_6_hsl = post_6_count / total_pixels) %>%
  mutate(ratio_full_red = full_red_count / total_pixels) %>%
  mutate(ratio_full_oragne = full_orange_count / total_pixels) %>%
  mutate(ratio_full_yellow = full_yellow_count / total_pixels) %>%
  mutate(ratio_full_green = full_green_count / total_pixels) %>%  
  mutate(ratio_full_cyan = full_cyan_count / total_pixels) %>%  
  mutate(ratio_full_blue = full_blue_count / total_pixels) %>%  
  mutate(ratio_full_purple = full_purple_count / total_pixels) %>%  
  mutate(ratio_full_mag = full_mag_count / total_pixels) %>%  
  mutate(ratio_full_red = full_red_count / total_pixels) %>%
  mutate(ratio_visib_red = visib_red_count / total_pixels) %>%
  mutate(ratio_visib_oragne = visib_orange_count / total_pixels) %>%
  mutate(ratio_visib_yellow = visib_yellow_count / total_pixels) %>%
  mutate(ratio_visib_green = visib_green_count / total_pixels) %>%  
  mutate(ratio_visib_cyan = visib_cyan_count / total_pixels) %>%  
  mutate(ratio_visib_blue = visib_blue_count / total_pixels) %>%  
  mutate(ratio_visib_purple = visib_purple_count / total_pixels) %>%  
  mutate(ratio_visib_mag = visib_mag_count / total_pixels) %>%
  mutate(ratio_vivid_red = vivid_red_count / total_pixels) %>%
  mutate(ratio_vivid_oragne = vivid_orange_count / total_pixels) %>%
  mutate(ratio_vivid_yellow = vivid_yellow_count / total_pixels) %>%
  mutate(ratio_vivid_green = vivid_green_count / total_pixels) %>%  
  mutate(ratio_vivid_cyan = vivid_cyan_count / total_pixels) %>%  
  mutate(ratio_vivid_blue = vivid_blue_count / total_pixels) %>%  
  mutate(ratio_vivid_purple = vivid_purple_count / total_pixels) %>%  
  mutate(ratio_vivid_mag = vivid_mag_count / total_pixels) %>%
  mutate(ratio_vivid = vivid_count / total_pixels)

Exploration

2D Scatter

• frequency of most common posterized color vs most common native color

fig <- plot_ly(imgsd_tidy, 
               x= ~post_top_count, 
               y= ~common_hsl_1_count, 
               type = "scatter", mode="markers", size = 2, color = ~sub_img)

fig

• Light min x light max

fig <- plot_ly(imgsd_tidy, 
               x=~light_min_val, 
               y= ~light_max_val, 
               type = "scatter", mode="markers", size = 2, color = ~sub_img)

fig

• Gen bright x gen dark

fig <- plot_ly(imgsd_tidy, 
               x=~gen_bright_count, 
               y= ~gen_dark_count, 
               type = "scatter", mode="markers", size = 2, color = ~sub_img)

fig

• Sat min x sat max

fig <- plot_ly(imgsd_tidy, 
               x=~sat_min_val, 
               y= ~sat_max_val, 
               type = "scatter", mode="markers", size = 2, color = ~sub_img)

fig

1D Histograms

• Vivid %

Due to a very large number of images that have fewer than 2% vivid pixels, Vivid Ratios are separated out into three segments: 0% vivid pixels, 0-1% vivid pixels, and more than 1% vivid pixels

vivid_ratio <- imgsd_ratio %>% select(ratio_vivid)
vivid_ratio$ratio_vivid <- as.numeric(vivid_ratio$ratio_vivid)

vivid_ratio <- vivid_ratio %>% mutate(
  ratio_rank = case_when(
    ratio_vivid == 0 ~ 0, 
    ratio_vivid > 0 & ratio_vivid < 0.01 ~ 1, 
    ratio_vivid >= 0.01 ~ 2)
  )

rr_counts <- count(vivid_ratio, ratio_rank)

vrr_pie <- plot_ly(rr_counts, labels=~factor(ratio_rank), values= ~n, type='pie')

vrr_pie

# 0 -> No Vivid Pixels
# 1 -> 0-1% vivid pixels
# 2 -> more than 1% vivid pixels

Less vivid pixels than expected! Way less! Only 359 images/subimages had more than 1% of pixels with more than 70% saturation and lightness between 40 and 70%

Now let’s get back to seeing the distribution of those 359 values:

vivid_hist <- vivid_ratio %>% filter(ratio_rank == 2)

fig <- plot_ly(vivid_hist,
               x= ~ratio_vivid,
               type = "histogram")

fig

Future investigation will perform these calculations on the main dataframe in order to access specific image IDs and evaluate the subjective qualities of the top vivid images.

• Post-num (filter by img segment)

Investigating the distribution of how many posterization “clumps” were in each image

#first setting up filters for more useful faceting going forward
r_fig_filter_0 <- imgsd_ratio %>% filter(imgsd_ratio$sub_img == 0)
r_fig_filter_a <- imgsd_ratio[imgsd_ratio$sub_img %in% c(1, 2, 3), ]
r_fig_filter_b <- imgsd_ratio[imgsd_ratio$sub_img %in% c(4, 5, 6), ]
r_fig_filter_c <- imgsd_ratio[imgsd_ratio$sub_img %in% c(7, 8, 9), ]


fig_0 <- ggplot(r_fig_filter_0,
               aes(x=post_num_regions)) + 
                geom_histogram(binwidth = 5)

fig_a <- ggplot(r_fig_filter_a,
              aes(x=post_num_regions)) + 
              geom_histogram(binwidth = 5) +
              facet_grid (~ sub_img)

fig_b <- ggplot(r_fig_filter_b,
              aes(x=post_num_regions)) + 
              geom_histogram(binwidth = 5) +
              facet_grid (~ sub_img)

fig_c <- ggplot(r_fig_filter_c,
              aes(x=post_num_regions)) + 
              geom_histogram(binwidth = 5) +
              facet_grid (~ sub_img)

fig_0b <- ggplot(r_fig_filter_0,
               aes(x=post_num_regions)) + 
                geom_histogram(binwidth = 50)

fig_0

fig_0b

fig_a

fig_b

fig_c

No huge conclusions to draw about the distribution in sub_image 0, other than the x-scale is shown as roughly 10x (slightly less) than the subimages. Also mildly interesting (also on sub_img 0), the max count for any given bin (at bin-width 5), is a fraction of the scale of the other sub_images. Bumping the sub_img 0 binwidth up to 50 (10x), brings it more in line with the counts in the sub_images, but the long tail on sub_img 0 keeps it from matching exactly.

Otherwise, the only noteworthy observation is the less-intense right skew on sub_images 2, 5, and 8.

These sub-images represent the horizontal middle third of their source images, mimicking the artistic principles of the rule of thirds and putting focal points near the center of the image.

• Exif brightness

EXIF data, I have not forsaken you.

fig <- ggplot(exif_tidy,
               aes(x=brightness_value)) + 
                geom_histogram(bins=250)

fig

That’s the most normal distribution we’ve seen yet! But still pretty irregular. Let’s see how it compares to the HSL data

• Mean_lightness

fig_all <- ggplot(imgsd_ratio,
               aes(x=light_mean_val)) + 
                geom_histogram(bins=250)

fig_0 <- ggplot(r_fig_filter_0,
               aes(x=light_mean_val)) + 
                geom_histogram(bins=250)

fig_a <- ggplot(r_fig_filter_a,
              aes(x=light_mean_val)) + 
              geom_histogram(bins=250) +
              facet_grid(~ sub_img)

fig_b <- ggplot(r_fig_filter_b,
              aes(x=light_mean_val)) + 
              geom_histogram(bins=250) +
              facet_grid(~ sub_img)

fig_c <- ggplot(r_fig_filter_c,
              aes(x=light_mean_val)) + 
              geom_histogram(bins=250) +
              facet_grid(~ sub_img)


fig_all

fig_0

fig_a

fig_b

fig_c

Observations: Variation among sub-images is fairly minor, with some some possibility that corner quadrants (1, 3, 7, 9) have wider distributions overall. Lightness values processed for this dataset are centered around 0.625 with a slight left skew. While the EXIF data has a less-normal distribution, it does seem to have a center slightly to the right of its baseline value, but the irregularity of the shape looks more like a right skew than left.

• (r/g/b) mean
  

fig <- plot_ly(imgsd_ratio, alpha = .4)
fig <- fig %>% add_histogram(x = ~r_mean)
fig <- fig %>% add_histogram(x = ~g_mean)
fig <- fig %>% add_histogram(x = ~b_mean)
fig <- fig %>% layout(barmode = 'overlay', colorway=c('red', 'green', 'blue'))

fig

Observation: No special information here. As expected, it looks a lot like the mean lightness value distrbution. Almost as if r+g+b = light….

• Date distribution (with and without year)

fig <- plot_ly(exif_tidy, x = ~date, type = 'histogram')

fig_all <- plot_ly(exif_tidy, x = ~full_date, type = 'histogram')

fig

fig_all

Observation: Even when adjusting for year, the distribution of images is highly irregular. As a month, August is over-represented, and as an individual date, Will and Taylor’s wedding is over-represented.

exif_tidy$time <- strptime(exif_tidy$time, format = "%H:%M%S")

fig <- plot_ly(exif_tidy, x = ~time, type = 'histogram')
fig

Error: C stack usage  15924272 is too close to the limit

Analysis

Final data prep!

Slimming down the EXIF data frame….

#slimming down exif columns....

simple_exif <- exif_tidy %>% select(c(flickr_id, date, month, time, software, jfifversion, brightness_value))

… and adding those EXIF columns to the main dataframe

simple_exif <- simple_exif %>%
  mutate(flickr_id = as.character(flickr_id))

# bringing it all full circle with this variable choice

all_img_data <- imgsd_ratio %>% 
  left_join(simple_exif, by = c("using_id" = "flickr_id"))

Warning: Detected an unexpected many-to-many relationship between `x` and `y`.

#this throws a warning about many-to-many relationships, but this is expected behavior

This space reserved for re-creating sub-frames for ‘faceting’

At last, let’s revisit those hypotheses

H1 - Hue vs Date

\(Ho:\) There is no correlation between time of year and color values

\(Ha:\) Warm color values are more prominent between May and September

Gut Check - Due to the uneven distribution of sample images over time, I don’t have a strong expectation of valid results.

exif_tidy$month <- as.integer(exif_tidy$month)

season_split <- exif_tidy %>% mutate(
  season = case_when(
    month >= 5 & month <= 9 ~ 1, TRUE ~ 0)
  )

season_counts <- table(season_split$season)
season_data <- data.frame(ratio = names(season_counts), count = as.vector(season_counts))

season_data

On the other hand, summer values (622) don’t outrageously outnumber non-summer values.

Now to collect the hue information we will be comparing

all_img_data <- all_img_data %>% 
  mutate(visib_warm = visib_red_count + visib_orange_count + visib_yellow_count + visib_mag_count) %>%
  mutate(visib_cool = visib_green_count + visib_cyan_count + visib_blue_count + visib_purple_count)
  
h1_frame <- all_img_data %>% 
  select(c(using_id, sub_img, total_pixels, visib_warm, visib_cool, date, month)) %>% 
  mutate(warm_ratio = visib_warm / total_pixels) %>% 
  mutate(cool_ratio = visib_cool/total_pixels) %>% 
  mutate(season = case_when(month >= 5 & month <= 9 ~ 1, TRUE ~ 0)) %>%
  mutate(ratio_diff = warm_ratio - cool_ratio)

Testing Time

t.test(warm_ratio ~ season, h1_frame)

    Welch Two Sample t-test

data:  warm_ratio by season
t = 11.179, df = 9078.6, p-value < 2.2e-16
alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
95 percent confidence interval:
 0.01619583 0.02308347
sample estimates:
mean in group 0 mean in group 1 
     0.04115762      0.02151798 

Despite my hesitation, the results of the T-test are strongly in favor of rejecting the null hypothesis that there is no difference in visible warmth throughout the year. A high t-value and low p-value are both in support of this conclusion.

H2 - Lightness vs Time

\(Ho:\) There is no correlation between time of day and lightness values

\(Ha:\) Lightness values are higher between 6 am and 6pm

h2_frame <- all_img_data %>% 
  select(c(using_id, sub_img, time, brightness_value, light_mean_val))%>% 
  mutate(daytime = case_when(time >= "06:00:00" & time <= "18:00:00" ~ 1, TRUE ~ 0))

H3 - Saturation vs Subject

\(Ho:\) There is no correlation between saturation and being a picture of my cat

\(Ha:\) Low saturation values are increasingly common over time, especially in central sub-images

H4 - Vividness vs Image Type

\(Ho:\) Vivid ratio (percentage of vivid pixels) is uniformly distributed among all Software types

\(Ha:\) Vivid ratio is consistently highest in Slow Shutter Cam photos without JFIF values

Conclusion